'5x7" film' is smaller than 5" x 7", at about 125x175mm. By 'nominal 5x7"' I meant 5" by 7", which would be 127x178mm - which coincidentally is very close to the standard size of 13x18cm film. And 5x7" paper really is 5" by 7", or the size of a 13x18cm film.
It's all back to those pesky cut sheet film adapters for glass plate holders. The glass plates were "full size", so that defined the outer dimensions of the film adapters. To fit inside the film needed to ba a few mm smaller than the outside of the sheath.